Mathematical vs Empirical Thought Experiments

If we take into account one of the most important differences between empirical and mathematical reasoning, we may be led to the conclusion that it is misleading and deceptive to speak of mathematical thought experiments. However, an important qualification of this claim seems in order. Although my first thesis holds true in its own sense, it is perhaps advisable to propose another sense of “mathematical thought experiment” in which we may talk about thought experiments in formal reasoning, following suggestions already present in the literature and avoiding too great divergence of epistemological reflections from the self-understanding of mathematicians. In this different sense, mathematical thought experiments might be regarded as a subset of visual proofs, based on diagrams. However – and this will be my third and final thesis –, the use of this sense of “TE” is harmless only under certain conditions.